matita/matita/contribs/RELATIONAL/NLE/props.ma

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  14
  15
  16
  17 include "NLE/order.ma".
  18
  19 theorem nle_trans_succ: ∀x,y. x ≤ y → x ≤ succ y.
  20  intros; elim H; clear H x y; autobatch.
  21 qed.
  22
  23 theorem nle_gt_or_le: ∀x, y. y > x ∨ y ≤ x.
  24  intros 2; elim y; clear y;
  25  [ autobatch
  26  | decompose;
  27    [ lapply linear nle_inv_succ_1 to H1
  28    | lapply linear nle_lt_or_eq to H1
  29    ]; decompose; destruct; autobatch depth = 4
  30  ].
  31 qed.